down
He was lying down on the bed.

there
He just lay there smiling.

comfortably, helplessly, limply, peacefully, quietly

on
She lay on her stomach.

in
She likes to lie in bed all day.

lie asleep, lie awake
I used to lie awake at night worrying about it.

lie dead, lie unconscious
A man lay dead in the middle of the road.

lie face down, lie prone (formal), lie prostrate (formal)
He was lying face down in the mud.

lie face up, supine (formal)
Lie face up with your feet on the floor.

lie flat
I was lying flat on the floor.

lie motionless, lie still
Lie still while I put the bandage on.

lie naked
She was still lying naked on the bed.

lie sprawled
She lay sprawled on the sofa.

convincingly
He was unable to lie convincingly.

easily
constantly, repeatedly
blatantly
deliberately, intentionally
completely, outright, totally (all AmE)

about
She lied about her age.

to
Don't lie to me.

lie through your teeth
lie under oath

Lie is used with these nouns as the subject:
challenge, corpse, crux, danger, destiny, difference, difficulty, dilemma, distinction, dust, explanation, farm, fog, greatness, guilt, hair, hand, hope, house, loyalty, mist, remains, route, shadow, snow, success, talent, taste, truth, value, weakness